Output and substitution elasticity estimates between renewable and non-renewable energy: implications for economic growth and sustainability in India

Abstract

The energy profile of India is dominated by fossil fuels, which create concerns over resource and environmental sustainability as fossil fuels are non-renewable and high carbon emitting. This scenario has necessitated the call for more renewables to replace fossil fuels to address resource and environmental sustainability concerns. This study, therefore, investigates the possibility of switching the fossil fuels of oil, coal, and natural gas for renewable energy in India. Using annual Indian data spanning more than four decades, a transcendental logarithmic production function based on a second-order Taylor Series approximation is estimated with the ridge regression technique. To achieve robustness, two equations with gross domestic product and adjusted net savings as regressands are estimated to proxy economic growth and sustainable development, respectively. The empirical results show substantial substitution possibilities between the fuels for both gross domestic product and adjusted net savings equations. The empirical findings show that India has the capacity to satisfy its energy needs through renewables to pursue not only economic growth but sustainable development. To actualize this potential, the Indian government should promote investment in renewables as this also promotes economic growth and development.

Appendices

Output elasticity

Given the general formula in equation (3), the output elasticity for the respective individual input

are given as follows:

Oil: ${\eta}_{ot}=\frac{\partial \ln {q}_t}{\partial \ln {o}_{ot}}={\alpha}_o+2{\alpha}_{oo}\ln {o}_t+{\alpha}_{or}\ln {r}_t+{\alpha}_{oc}\ln {c}_t+{\alpha}_{og}\ln {g}_t,$(1b)

Gas: ${\eta}_{gt}=\frac{\partial \ln {q}_t}{\partial \ln {g}_{gt}}={\alpha}_g+2{\alpha}_{gg}\ln {g}_t+{\alpha}_{gr}\ln {\alpha}_t+{\alpha}_{gc}\ln {c}_t+{\alpha}_{go}\ln {o}_t,$(2b)

Coal: ${\eta}_{ct}=\frac{\partial \ln {q}_t}{\partial \ln {c}_{ct}}={\alpha}_c+2{\alpha}_{cc}\ln {c}_t+{\alpha}_{cr}\ln {r}_t+{\alpha}_{cg}\ln {g}_t+{\alpha}_{co}\ln {o}_t,$(3b)

Renewable: ${\eta}_{rt}=\frac{\partial \ln {q}_t}{\partial \ln {r}_{rt}}={\alpha}_r+2{\alpha}_{rr}\ln {r}_t+{\alpha}_{rc}\ln {c}_t+{\alpha}_{rg}\ln {g}_t+{\alpha}_{ro}\ln {o}_t,$(4b)Where η_ot, η_gt, η_ct, and η_rt respectively stands for the elasticity of output for oil, gas, coal, and renewable energy.

Substitution elasticity

From the general equation given in (5), the specific substitution elasticity between two input fuels are given as follows:

$$ {\sigma}_{go}={\left[1+2\left[{\alpha}_{go}-{\alpha}_{gg}\left({\eta}_o/{\eta}_g\right)-{\alpha}_{oo}\left({\eta}_g/{\eta}_o\right)\right].{\left[{\eta}_g+{\eta}_o\right]}^{-1}\right]}^{-1}, $$

(1c)

$$ {\sigma}_{co}={\left[1+2\left[{\alpha}_{co}-{\alpha}_{cc}\left({\eta}_o/{\eta}_c\right)-{\alpha}_{oo}\left({\eta}_c/{\eta}_o\right)\right].{\left[{\eta}_c+{\eta}_o\right]}^{-1}\right]}^{-1}, $$

(2c)

$$ {\sigma}_{cg}={\left[1+2\left[{\alpha}_{cg}-{\alpha}_{cc}\left({\eta}_g/{\eta}_c\right)-{\alpha}_{gg}\left({\eta}_c/{\eta}_g\right)\right].{\left[{\eta}_c+{\eta}_g\right]}^{-1}\right]}^{-1}, $$

(3c)

$$ {\sigma}_{ro}={\left[1+2\left[{\alpha}_{ro}-{\alpha}_{rr}\left({\eta}_o/{\eta}_r\right)-{\alpha}_{oo}\left({\eta}_r/{\eta}_o\right)\right].{\left[{\eta}_r+{\eta}_o\right]}^{-1}\right]}^{-1}, $$

(4c)

$$ {\sigma}_{rg}={\left[1+2\left[{\alpha}_{rg}-{\alpha}_{rr}\left({\eta}_g/{\eta}_r\right)-{\alpha}_{gg}\left({\eta}_r/{\eta}_g\right)\right].{\left[{\eta}_r+{\eta}_g\right]}^{-1}\right]}^{-1}, $$

(5c)

$$ {\sigma}_{rc}={\left[1+2\left[{\alpha}_{rc}-{\alpha}_{rr}\left({\eta}_c/{\eta}_r\right)-{\alpha}_{cc}\left({\eta}_r/{\eta}_c\right)\right].{\left[{\eta}_r+{\eta}_c\right]}^{-1}\right]}^{-1}, $$

(6c)

Where σ_go measures elasticity of substitution between gas and oil, σ_co is between coal and oil, σ_cg is between coal and gas while the elasticities between renewable energy and oil, renewable energy and gas, and between renewable energy and coal are respectively measured by σ_roσ_rgandσ_rc.